3. Assuming that the average FOX viewer is probably overweight,

and that a "fat wisecrack" would indirectly insult their overweight audience... I am reluctant to say it was a deliberate jab at your weight.
But, it could be one or two people at FOX who chose those words just to be snide, and it got past the bosses. Probably impossible to know for sure.

6. an interesting experience

less than half an hour after receiving an email, a driver was at my door. I sat in a room alone with an earbud in my right ear and tried to talk to a camera I couldn't even see. I'll try to be better next time. I've only done NPR before.